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Abstract

Common randomness arising from turbulence-induced signal fading in reciprocal optical wireless channels is a beneficial resource that can be used to generate secret keys shared by two legitimate parties. The concept of optical wireless channels using common-transverse-spatial-mode coupling (CTSMC) that can maintain perfect fading reciprocity in atmospheric turbulence is first developed in a general manner. Subsequently, by performing Monte Carlo simulations, the Johnson SB probability distribution is demonstrated to be appropriate for statistical description of turbulence-induced signal fading in an optical wireless channel constructed by use of two identical CTSMC transceivers, and the nature of correlation between signal fadings detected by two contiguous reception spatial modes is further quantitatively characterized, revealing that rapid spatial decorrelation between signal fadings observed by a legitimate party and an eavesdropper holds for scenarios of practical interest. Finally, the information theoretic capacity for generating secret keys from CTSMC-based optical wireless channels is theoretically formulated and quantitatively examined under different conditions, manifesting that the turbulence strength and average electrical signal-to-noise ratio have a noticeable combined impact on the secret key capacity, especially in the far-field case.

Figures (4)

Fig. 1 Schematic diagram of a bidirectional optical wireless channel with each terminal transmitting and receiving wave fields in a common transverse spatial mode; ΨA(rA) and ΨB(rB) therein are the common transverse spatial modes used by Alice’s and Bob’s terminals, respectively, which are not necessarily identical; rA and rB represent a two-dimensional point in the transverse planes at z = 0 and z = L, respectively. An eavesdropper called Eve separated from Alice by distance d is equipped with a receiving aperture centered at point rE; α is the angle that the z-axis makes with the line from point o′ to point rE.

Fig. 3 Scaled spatial correlation distance as a function of log10 (qc) with qw ≡ 0.2 and different L. The asterisks and circles denote values calculated according to numerical simulation results and the curves represent the fit of a smoothing spline to the values obtained from the numerical simulation results.

Fig. 4 Secret key capacity in terms of the base-10 logarithm of the average electrical SNR with different qc. The noise variances at Alice’s and Bob’s terminals take the same value. ϑA ≡ ϑB = ϑ. (a) the far-field case with qw ≡ 0.2; (b) the transition case with qw ≡ 2; (c) the near-field case with qw ≡ 20.